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The following type of Carleman estimate is known to be true on a certain range of $p,q$: \\[ \\|e^{v\\cdot x}u\\|_{L^q(\\mathbb{R}^d)} \\le C\\|e^{v\\cdot x}P(D)u\\|_{L^p(\\mathbb{R}^d)} \\] with $C$ independent of $v\\in \\mathbb{R}^d$. The estimates are consequences of the uniform Sobolev type estimates for second order differential operators due to Kenig-Ruiz-Sogge \\cite{KRS} and Jeong-Kwon-Lee \\cite{JKL}. The range of $p,q$ for which the uniform Sobolev type estimates hold was completely characterized for the second order differentia"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.03040","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-08T11:08:33Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"4dac14d75fea9405ec91c24530a0fe98fd010601e975cc9e4737c4c71479e402","abstract_canon_sha256":"64d6d4c6c3bff0f07b0fb954d38138a2f84bc04b477960948670321d35004c71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:44.642452Z","signature_b64":"I4cwp8og8D9LIomBzsj2Cv3RB0mFP4iUpO/JH+PEg91qrd3DOZU5qj2/tufv7ptADWPFb9twCsgg2Qg3CfAfBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9948a5808d516be99eada33f45d2a72ac19d8c29142a224eda8ca0c8cae2868d","last_reissued_at":"2026-05-18T00:21:44.641953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:44.641953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Carleman estimates and boundedness of associated multiplier operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Eunhee Jeong, Sanghyuk Lee, Yehyun Kwon","submitted_at":"2018-03-08T11:08:33Z","abstract_excerpt":"Let $P(D)$ be the Laplacian $\\Delta,$ or the wave operator $\\square$. 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